A077768 Number of times that the sum of two squares is an integer between n^2 and (n+1)^2; multiple representations are counted multiply.

1, 2, 2, 3, 4, 4, 6, 7, 7, 7, 8, 10, 10, 11, 11, 12, 13, 15, 15, 14, 18, 17, 17, 19, 19, 21, 20, 21, 23, 22, 26, 25, 26, 27, 25, 29, 27, 32, 30, 28, 33, 33, 36, 34, 33, 37, 36, 39, 38, 40, 39, 38, 42, 40, 46, 43, 45, 44, 46, 48, 47, 49, 50, 48, 50, 50, 53, 55, 52, 55, 53, 60, 57

Offset

1,2

Comments

Related to the circle problem, cf. A077770. Note that 2*a(n)-A077770(n)/4 is the characteristic sequence for the Beatty sequence A001951. See A077769 for a more restrictive case. A077773 counts multiple representations only once.

Links

Table of n, a(n) for n=1..73.

Example

a(8)=7 because 65=64+1, 65=49+16, 68=64+4, 72=36+36, 73=64+9, 74=49+25 and 80=64+16 are between squares 64 and 81. Note that 65 occurs twice.

Mathematica

maxN=100; lst={}; For[n=1, n<=maxN, n++, cnt=0; i=n; j=0; While[i>=j, j=1; While[i^2+j^2<(n+1)^2, If[i>=j&&i^2+j^2>n^2, cnt++ ]; j++ ]; i--; j-- ]; AppendTo[lst, cnt]]; lst

Crossrefs

Cf. A001951, A077769, A077770.

Sequence in context: A114093 A345141 A239950 * A143038 A029040 A053281

Adjacent sequences: A077765 A077766 A077767 * A077769 A077770 A077771

Keyword

nonn

Author

T. D. Noe, Nov 20 2002

Status

approved